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200 games were played, resulting in a 71%-29% split. Is this significant? (What would a statistical analysis tell us the Confidence Interval (CI) was for 200 games, Chi^2 analysis, etc.)

This game was played only 2-players. Would a 3-player+ game result in similar two times more likely for a thinking player to win?

This Basic Player still made random plays, unless taking those actions would immediately win them the game (example if the standard rules, Draw 1 and Play 1, a basic player would not play one of the cards Keeper:Dog, Keeper:Tree, and the Goal:Walk the Dog even if all of them were in their hand, because they wouldn't win immediately.) Are the results of this experiment similar to the results you would have from a game with no luck, but similar 2-card win goals?

To expand on the last point, imagine a game where each player had access to all of the cards in the Fluxx, and was allowed to "draw" the card of their choosing. Would a Basic Player in this game of no luck have a similar win percentage?

To me Fluxx is self-evidently a game where there's a little bit of skill and strategy, but a great big helping of luck. I'll be interested if anyone can come up with any answer that's more substantial than that!
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thesunneversetsJan 9 '13 at 12:19

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I think you might have to expand on that last point a bit. If I could draw whatever I want, I would draw Play 3/Love/All You Need Is Love in my starting hand.
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KristoJan 9 '13 at 14:21

@Kristo, I admit my question comes from an unfamiliarity with the cards in the deck. I am having a hard time envisioning a non-luck version of this game, that cannot be instantly won. What I am trying to determine is if some such no-luck version existed, why wouldn't te win% look something like a 2:1 ratio?
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user1873Jan 9 '13 at 15:15

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As to your first question, a result as extreme as 71%-29% over a range of 200 games will occur on average exactly 259038549769305536821652665944548563501370191596359 out of every 200867255532373784442745261542645325315275374222849104412672 experiments, or roughly 0.000000129% of the time, if the process were a coin toss. So we can reject that hypothesis out of hand for any reasonable level of significance. (Source: "Statistics:-CDF(Binomial(200, 1/2), 2*29);" in Maple.)
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Erik P.Jan 14 '13 at 22:28

2 Answers
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There's a modicum of skill involved. You can do some things to increase the odds that random draws will go your way. Any or all of these could be used to augment Basic Player's behavior.

Recognize that some keepers appear more often in goals. Prioritize The Brain and generally anything to do with food.

Playing keepers toward the current goal is usually a waste of time, especially with lots of players. The goal may change several times before your next turn.

Avoid Draw X rules when you don't have Play X to back it up. Otherwise you hand all your opponents extra card draw before your next turn. A fistful of cards increases your chances of going off on your next turn, but it does so for everybody at the table. Risk/reward.

Play your cards in the proper order, e.g., by not reducing/trashing the current Play rule before you've played all your cards.

Hang on to cards like Let's Do That Again and Take Another Turn until the board has some favorable Draw and Play rules. Setting up a Dominion-style 5-minute turn is soooo much fun.

Ultimately, Fluxx is a fun game because of the crazy combinations that make everyone's heads spin. Actively trying to win is of lesser importance. In my opinion, the better skill to master is to make sure you don't make the game boring for everyone else:

Hand Limit 0 is an awesome card, provided you still have plays left for yourself to change it before your turn ends. Draw 1/Play 1 with 0-card hands is painful.

Play All with Draw 1 is similarly bad, though it gets less painful with more opponents.

A fortunate deal can give you the game, but only if you have the ability to play it correctly. Continually getting the 'wrong' cards can mean that you'll never win, but a skilled player can mitigate that.

You can't look at the colour grey and ask if it's black or white. It might be more black than white, or closer to white than to black, but you can't say that it's definitively one or the other.

A game cannot be both a game of skill and luck, as the two are mutually exclusive. By your logic, poker is a game of both skill and luck. The definition of a game of luck is that there is no strategy that will increase your odds of winning. Most games have a random element involved but are true games of skill. In fact, one of the greatest skills of a player is making choices that remove elements (consider Magic the Gathering). I don't want to be all William Blake/CS Lewis on you, but the two are mutually exclusive. Having random elements in a game does not make it a game of luck.
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corsiKaJan 9 '13 at 21:44

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Poker is both a game of skill and a game of luck. Individual hands are heavy on luck (influenced by your skilled decisions to draw, bluff, fold, and how you raise), but over the course of many hands, it's a game of skill (But still with a wee bit of luck in it; it's quite possible to draw bad hands all night, just unlikely). If you insist that every game is either skill or luck, then every game is skill - with the sole exception of Hi Ho Cherry-O.
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Paul MarshallJan 25 '13 at 17:22